Classical characters of spinor fields in torsion gravity

TL;DR

This paper explores the derivation of Mathisson-Papapetrou-Dixon equations from the Dirac equation within torsion gravity, revealing their trivial form under plane wave assumptions.

Contribution

It provides a general derivation of MPD equations from the Dirac equation on manifolds with torsion, highlighting their triviality in plane wave scenarios.

Findings

MPD equations derived from Dirac equation on torsion manifolds

In plane wave cases, MPD equations become trivial

General formulation applicable to relativistic quantum mechanics with hydrodynamic variables

Abstract

We consider the problem of having relativistic quantum mechanics re-formulated with hydrodynamic variables, and specifically the problem of deriving the Mathisson-Papapetrou-Dixon equations from the Dirac equation. The problem will be answered on a general manifold with torsion and gravity. We will demonstrate that when plane waves are considered the MPD equations acquire the form given in [1], but we will also see that in such a form the MPD equations become trivial.